Abstract

The use of successive resonances for ion ejection is demonstrated here as a method of scanning quadrupole ion traps with improvement in both resolution and sensitivity compared with single frequency resonance ejection. The conventional single frequency resonance ejection waveform is replaced with a dual-frequency waveform. The two included frequencies are spaced very closely and their relative amplitudes are adjusted so that the first frequency that ions encounter excites them to higher amplitudes where space charge effects are less prominent, thereby giving faster and more efficient ejection when the ions come into resonance with the second frequency. The method is applicable at any arbitrary frequency, unlike double and triple resonance methods. However, like double and triple resonance ejection, ejection using successive resonances requires the rf and AC waveforms to be phase-locked in order to retain mass accuracy and mass precision. The improved performance is seen in mass spectra acquired by rf amplitude scans (resonance ejection) as well as by secular frequency scans.

Keywords

Introduction

Since the quadrupole ion trap was first proposed in the early fifties by German physicist and later Nobel Laureate Wolfgang Paul [1], many methods of mass spectral acquisition using ion traps have been demonstrated. A key development was the mass selective instability scan [2]. With this technique, a mass spectrum can be obtained by scanning ions sequentially out of the trap in order of increasing m/z (mass/charge ratio, also Thomson, Th) by ramping the amplitude of the driving radiofrequency (rf) waveform. The rf ramp causes ion trajectories to become unstable in one or more dimensions as the ions are brought to the working point (e.g., qz = 0.908) where qz is the classic Mathieu parameter for the z axis, and the z-instability allows the ions to be detected externally [3].

Later, an alternative method of ion trap scan out was demonstrated. The method, which was termed “resonance ejection” [4, 5, 6, 7], uses a small supplementary AC signal to impose a second working point or “hole” on the q axis (more precisely, on an iso-β line) of the Mathieu stability diagram. The ions can then be scanned through the operating point and ejected in order of increasing m/z as the rf amplitude is increased, which generally results in increased resolution compared with boundary ejection. Alternatively, the “hole” can be scanned through all possible q values by ramping the frequency of the supplementary AC at fixed rf amplitude in what has been termed a “secular frequency scan” [8, 9, 10, 11, 12].

Resonance ejection is based on parametric (quadrupolar) or dipolar excitation of ions at a characteristic mass/charge-dependent oscillation frequency. The available set of frequencies includes (1) the fundamental secular frequency ⍵u,0 in radians/sec, (2) higher order quadrupolar resonances, (3) higher order resonances of other even and odd multipole components, (4) harmonics of the secular frequency, and (5) combination frequencies such as sideband frequencies. The secular frequency, the primary ejection driver in most resonance methods, can be calculated from the Mathieu parameter βu (0 ≤ βu ≤ 1) [3, 13], Equation 1:

$$ {\upomega}_{\mathrm{u},0} = {\upbeta}_{\mathrm{u}}\varOmega /2 $$

(1)

where u is a characteristic dimension (r =√(x2+y2), or z) and Ω is the angular rf frequency. However, higher order resonances also exist, including higher order quadrupolar resonances, ⍵u,0 [14, 15], which occur where n = 0 in Equation 2

with K being the order of the resonance and n being an integer. Harmonics at, for example, 2⍵u,0 and 3⍵u,0, are also observed. All these resonances are known to be substantially weaker than the fundamental resonance and are thus not commonly sought or observed, as described in Franzen’s series of papers on the nonlinear ion trap [16, 17, 18, 19].

Franzen also described hexapolar, octopolar, and other higher order resonances. The general resonance condition is (Equation 3)

where r and z are the radial and axial dimensions, respectively, nr and nz are nonnegative integers, nr is even or zero, and nz is either even or odd (due to ion trap symmetry) [16]. The general resonance condition for the first stability region can equivalently be described in the frequency domain by [18] (Equation 4)

where nr, nz, and ν are positive integers restricted by the conditions that, for traps of axial symmetry, nr is even and nz is even for even multipoles and any integer for odd multipoles. For example, βz = 2/3 (nr = 0, nz = 3) corresponds to hexapole, decapole, and tetradecapole resonances. Hexapole resonances also occur at βu = 1/3, 1/2, and 2/5 [18]. An octopole resonance appears at βu = 1/2 [13], but the resonance is self-quenching (unless the frequency is being scanned appropriately) because the frequency of ion motion shifts substantially with the distance from the trap center. Positive frequency shifts are observed for a positive octopole contribution since the field strength near the electrodes increases faster than a pure quadrupole field. In contrast, negative shifts are observed for a negative octopole, whereas odd-order multipoles always decrease ion oscillatory frequencies because of their asymmetry, which causes ions to occupy regions of lower field strength [20, 21].

Franzen showed that ion ejection at a nonlinear resonance point greatly increases mass resolution, and this capability was incorporated into the commercial Bruker Corporation Esquire series of ion trap instruments. The scan was termed a “double resonance ejection” because of the co-occurrence of the dipolar excitation and the hexapolar (or octopolar) nonlinear resonance [22]. The effect of the hexapolar or octopolar resonance is to make the rate of ion ejection faster than the normal linear growth in amplitude with time, thus resulting in better resolution [13]. The effect has also been demonstrated in a micro-ion trap by the Ramsey group [22, 23]. A similar triple resonance scan mode has been patented by Varian [24, 25]. The method is procedurally similar to double resonance ejection, where double resonance is achieved by parametric excitation at the hexapole resonance, and the triple resonance is realized by simultaneously applying a dipolar waveform at the lower sideband (Ω - ⍵u) corresponding to the hexapolar resonance, again at βu = 2/3. Other sidebands, which generally occur at nΩ ± m⍵u, n and m being positive integers, may also be interrogated, but their magnitudes diminish with increasing n and m.

Multiple resonances may also be imposed on different regions of the Mathieu stability diagram. For example, in compressive resonance ejection [26], multiple resonance waveforms are used to impose several “holes” of instability on the q axis. The rf amplitude is ramped, causing multiple populations of ions to be ejected at each time point. The mass spectrum can then be mathematically calculated by using an algorithm to decompress the data. Rhombic ion ejection can also be performed by exciting ions simultaneously in orthogonal directions [27]. Because the ions being ejected travel around the rest of the ion cloud rather than through it, space charge effects are decreased and resolution is improved.

Here, successive excitation and ejection is described and demonstrated for the resonance ejection rf amplitude scan method [4, 5, 6, 7]. It is later shown for the secular frequency scan method of recording mass spectra [8, 9, 10, 11, 12, 28]. The successive resonance variant improves performance in both cases. In the successive resonance scan, a first supplementary AC frequency is given a low amplitude in order to excite ions to higher orbits in the ion trap, and a second, slightly higher frequency is given a higher amplitude in order to swiftly eject the excited ions. The sum of these two frequencies is applied to the ion trap in a dipolar fashion. While the spacing between the successive resonances needs to be fixed in order to obtain good results, the set of frequencies can be placed at any location on the q axis of the Mathieu stability diagram. The method retains the increase in resolution that has been previously demonstrated in resonance ejection variants but is more versatile because it does not require higher order field contributions, as do double and triple resonance ejection.

Instrumentation

All experiments were performed using a Thermo LTQ XL linear ion trap mass spectrometer interfaced to an Orbitrap (San Jose, CA, USA). The rf frequency was tuned to 1175 kHz. For resonance ejection with a fixed excitation frequency and an rf scan, the built-in scan function was used but, unless otherwise specified, the resonance ejection signal was replaced with an AC waveform of specified frequencies and amplitudes. The waveform was supplied by a Keysight 33612A arbitrary waveform generator (Newark, SC, USA). For successive resonance ejection, two channels on the generator were set to different frequencies and summed into a single channel. One frequency was less than half the driving rf frequency (i.e., a secular frequency) and the other was set to a frequency less than ~15 kHz from the first frequency (or the corresponding lower sideband Ω - ⍵, where ⍵ represents the secular frequency). General frequencies were 490 and 501 kHz, with the former having a smaller amplitude (~1 Vpp versus ~4 Vpp). With a resonance frequency of ~490 kHz, the scan rate of the instrument was ~16,666 Da/s.

Successive resonance secular frequency scanning was similarly performed in the secular frequency scan mode with the rf amplitude held sensibly constant. This was achieved over a period of 1 s using the Ultrazoom scan mode instead of the desired fixed rf amplitude because the LTQ instrument will only record data during an rf scan and the choice of the Ultrazoom scan minimizes the change in rf amplitude, thus limiting the (undesired) change in ion secular frequency. The same waveforms were applied in the successive resonance secular frequency scans but their frequencies were ramped linearly with time from high to low frequency (low to high mass). All auxiliary waveforms were triggered at the beginning of the mass scan with the trigger tools in the LTQ Tune diagnostics menu and were phase-locked to the rf frequency.

Mass calibration was performed by visually comparing the results of the successive resonance experiment with those obtained by analyzing each solution with the built-in resonance ejection scan (which was mass calibrated with Pierce ESI LTQ calibration solution using the built-in automatic calibration procedure). Resolution is reported as m/Δm, where Δm is the full width at half maximum (FWHM).

Results and Discussion

Successive resonance ejection at arbitrary frequencies can be accomplished by synthesizing a single dipolar waveform with two frequency components. The first frequency is set to any arbitrary frequency, in contrast to previous reports of double [22] and triple [24] resonance, which were performed only at nonlinear resonance points. The second frequency is set on a frequency that corresponds to a Mathieu q value that is close to the first frequency (in our case, ~10 kHz higher than the first frequency). As an example, with a driving rf frequency of 1.2 MHz, the two frequency components would be an arbitrarily chosen frequency of 490 kHz with an amplitude of ~1 Vpp and a second frequency at 501 kHz with an amplitude of ~5 Vpp. Alternatively, a lower rf sideband frequency of 1200 - 501 = ~699 kHz (Ω - ⍵) may be used. Note that the optimal difference between the two frequencies will vary with pressure, AC amplitude, and rf amplitude scan rate.

The first resonance that ions encounter during the rf ramp is used to excite ions to higher amplitudes. The amplitude of this particular frequency component is deliberately kept low to excite ions but prevent ion ejection, which would result in ghost peaks. The second frequency is set ~10 kHz higher and has a higher amplitude so that the excited ions are swiftly ejected from the trap. The frequency difference increases approximately linearly with scan rate and also varies slightly with the relative AC amplitudes. The result of the successive resonance phenomenon is improved sensitivity and resolution. As we will discuss later, this appears to be, at least in part, due to a mitigation of space charge effects.

A comparison of resolution and sensitivity in single and successive resonance ejection is given in Figure 1. The blue trace shows a standard single resonance ejection spectrum of three quaternary ammonium ions (m/z 284, 360, 382), whereas the red trace shows a successive resonance ejection scan using frequencies of 490 and 501 kHz. Both resolution (reported as m/Δm) and sensitivity (reported as total ion current, TIC) are marked. Resolution is significantly improved in the successive resonance scan, reaching more than a 3× improvement. Sensitivity is also improved, which is indicated by the increase in total ion current and peak height. The experiment was repeated at other frequencies, with similar improvements noted. Resolution was always 2–3× better than the single resonance scans and TIC increased, on average, by 15%–20%. Note that although the amplitude in the successive resonance scan is higher, a higher amplitude than 3 Vpp did not noticeably increase resolution in the single resonance ejection scan.

Successive resonances for ion ejection from an ion trap. The blue trace shows a single resonance ejection spectrum for a mixture of three quaternary ammonium ions (m/z 284, 360, and 382) using a 3 Vpp resonance ejection waveform at 490 kHz, whereas the red trace was obtained using successive resonance ejection with waveforms of 490 kHz, 1 Vpp, and 501 kHz, 5 Vpp. The scan rate in both experiments was approximately the same (~16,666 Da/s). Note that higher AC amplitudes in the single resonance ejection scan did not increase resolution. TIC = total ion current R = resolution

Now we take a moment to discuss the mechanism by which resolution is improved. In double and triple resonance ejection, resolution is improved when setting the resonance ejection frequency at a nonlinear resonance point, as discussed before. The co-occurrence of the excitation frequency and nonlinear resonance causes the ions to experience a rate of change of amplitude in the trap (that is, how far the ion is from the quadrupole center) that is faster than linear (see Refs. [18, 24, 29]), which is the rate of change that is usually observed when resonantly exciting ions. The mechanism of successive resonances, however, differs because nonlinear field resonances are not used and therefore not necessary. Instead, the ions are excited just before they are ejected. Because they are excited, (1) they are closer to the edge of the trap and therefore ejected faster than they would be if they occupied the center of the ion trap, (2) space charge is largely mitigated because the ion’s trajectory has time to recover from space charge effects that are very prominent at the trap center, where the rest of the ion cloud resides, and (3) the effects of non-linear fields are increased, assisting in ion ejection.

The major contribution of mechanism (2) is indicated by the resolution improvement with respect to m/z throughout most of the spectra presented here. If mitigation of space charge effects is a primary driver of resolution improvement, we expect the resolution improvement to decrease with m/z since the ions are being ejected in order of increasing m/z. That is, lower mass ions experience the greatest space charge effects since (1) they are ejected first when the ion cloud is dense, and (2) they unfortunately occupy the center of the ion cloud [30] and must be ejected through the distribution of higher m/z ions. Looking at Figure 1, we see that the resolution for m/z 284, the first ion ejected in the scan and, thus, the one subjected to the most space charge, is increased by approximately a factor of 4. The second ion ejected, m/z 360, experiences a factor of 3 increase in resolution, and the last m/z ejected, m/z 382, shows an increase in resolution of a factor of 1.5. Rhombic ion ejection, in which the ions are excited in both x and y, also reduces space charge effects because the ions being ejected circle the rest of the ion cloud [27].

A further note should be added regarding the isotopic distributions observed in the successive resonance scan. The distribution in the two scans differs slightly, which we attribute to the different phase relationship between the rf and two excitation waveforms. However, further studies will need to be performed in order to understand the effect of phase on isotope distributions.

Table 1 compares the resolution obtained from single and successive resonance ejection using an Ultramark 1621 calibration solution. For these scans, a lower sideband frequency corresponding to Ω - ⍵ was used in place of the second (higher amplitude) resonance frequency. On average, resolution is more than tripled from the classic single frequency resonance ejection scan. Also advantageous is the simplicity of the successive experiment since (1) no higher order resonances are needed and (2) only a single dipolar waveform is used, in contrast to triple resonance with parametric and dipolar excitation. The peak width improvement is similar to triple resonance ejection, despite the lack of the hexapolar resonance [24].

Table shows resolution, measured at 50% peak height (FWHM), for several peaks in the Ultramark 1621 calibration solution obtained by single and successive resonance ejection at β = 0.83. Improvement factor is defined as the ratio of the mass resolutions obtained at each of the successive resonance and single resonance ejection methods.

The new method may be advantageous due to its versatility since any arbitrary frequency can be used for ejection. Figure 2 demonstrates successive resonance ejection at 300, 400, and 500 kHz (βz = 0.51, βz = 0.68, and βz = 0.85), all of which show exceptional resolution compared with the built-in resonance ejection scan of the commercial LTQ instrument (solid purple trace). The resolution at 400 and 500 kHz is superior since the ejection qz is more optimal than at low q values, which is a well-known phenomenon.

Successive resonance ejection using sideband frequencies. Plot shows m/z 284 and its carbon isotope peak for successive resonance ejection at the specified frequencies (secular frequency/lower sideband frequency). The analytes were quaternary ammonium ions m/z 284, 360, and 382. The rf amplitude was ramped from m/z 50 to m/z 1000 during a normal LTQ mass scan. In the successive resonance experiments, the given frequencies were summed together (4 Vpp each) on an external function generator and applied to the linear trap as a single ejection waveform. Solid purple trace shows resonance ejection using the LTQ’s built-in normal scan function. Results are single scans

When performing successive resonance ejection, the resonance waveforms must be carefully matched experimentally, both in terms of amplitude and frequency. We noticed peak splitting and “ghost” peaks with many different combinations of scan rate, AC amplitudes, and frequencies. Careful tuning of each parameter must be performed in order to obtain good peak shape and avoid ghost peaks.

The AC waveforms in successive resonance ejection should also be phase-locked to the rf to ensure that the field strength at any given time is consistent from scan to scan [24, 31]. Although single scan resolution is improved without phase-locking, we consistently observed peak splitting and peak jumps, resulting in the precision of the mass measurements being decreased in many cases, as shown in Figure 3, which compares the relative standard deviation of the measured mass for 15 single resonance ejection spectra with 15 successive resonance ejection spectra (all performed using an LTQ XL). These experiments were performed with or without phase-locking and with either two secular frequencies (less than half the driving frequency) or with a secular frequency and a sideband frequency (rf frequency minus secular frequency). When the AC and rf were phase-locked and when only secular frequencies were used, mass precision was maintained. Figure 3b shows an average of 45 mass scans using 490 + 501 kHz, phase-locked to the rf, indicating that both resolution and mass accuracy/precision are maintained. However, when the AC and rf frequencies are not phase-locked (Figure 3c, average of 45 scans) or when sideband frequencies are used (Figure 3a, 500/693 kHz, where 693 kHz is the sideband frequency corresponding to a secular frequency of 500 kHz), peak splitting and poor mass precision are observed. Surprisingly, even when the sideband frequencies were phase-locked, good mass precision could not be obtained (although single scan resolution was still improved). The cause of this is not currently understood.

Effect of phase-locking on mass precision in single and successive resonance ejection. (a) Mass precision of single and successive resonance ejection on an LTQ XL with and without phase-locking, (b) average of 45 scans for a phase-locked successive resonance ejection experiment (490/501 kHz), and (c) average of 45 scans for a successive resonance ejection experiment (490/501 kHz, 3 Vpp) without phase-locking

There are two other variants of successive resonances for ion ejection. Up to this point, we have only discussed the first variant, wherein two closely spaced resonance frequencies corresponding to secular frequencies are summed together to create a dual frequency resonance ejection waveform. The rf amplitude is ramped so that ions first experience an excitation and then are ejected by the second frequency. The second variant, which also utilizes an analytical rf amplitude ramp, uses amplitude modulation to create a set of three closely spaced AC frequencies that are used for successive resonance ejection. Lastly, the third variant is a successive resonance secular frequency scan. Normally, in a secular frequency scan, the rf amplitude is kept constant while the resonance ejection frequency is ramped in order to eject ions in order of m/z. In the successive resonance secular frequency scan, the secular frequencies of ions are kept constant while two closely spaced AC frequencies (summed together) are both ramped linearly with time. The three variants described are presented in Table 2.

The second variant, in which amplitude modulation of the supplementary AC waveform produces successive resonance frequencies, is now discussed. The appropriate modulation frequencies were determined experimentally, and the resulting increase in resolution was almost 3-fold (Figure 4). In general, the carrier and modulating frequencies were chosen so that the resulting frequency spectrum contained components at ~480 kHz and ~490 kHz, the former being used for excitation and the latter being used for ejection. For example, in Figure 4c, a 490 kHz resonance ejection signal was modulated at 10 kHz, giving frequency components at 480, 490, and 500 kHz. An average of 14 scans is shown for this case, illustrating that mass precision is excellent. Both secular and sideband frequencies were successively utilized. Mass precision could be retained when using only secular frequencies and phase-locking the AC frequencies to the rf but not when using sideband frequencies (single scan shown in Figure 4b).

Successive resonance ejection by amplitude modulation. (a) Shows single resonance ejection during a normal LTQ scan from m/z 50 to m/z 1000 with a single resonance frequency of 450 kHz at 6 Vpp; (b) shows a successive resonance scan by modulating the amplitude of the 450 kHz waveform at 884 kHz with a 100% modulation depth (an amplitude modulation setting on the waveform generator); (c) is the result of amplitude modulation of a 490 kHz signal with a 10 kHz signal and is the average of 14 scans. Analytes were quaternary ammonium ions m/z 284, 360, and 382

Successive resonances can similarly be used to improve the resolution in secular frequency scanning, which we have previously characterized as a simple and interesting alternative to ramping the rf amplitude [10, 12, 28]. In the secular scan method, the frequency of the auxiliary AC signal is ramped to eject ions when their static secular frequencies match the varying AC frequency. In other words, the “hole” on the Mathieu stability diagram imposed by the supplementary AC is scanned, while the rf amplitude is constant, whereas in resonance ejection ions are scanned through the hole by ramping the rf amplitude, which increases ion secular frequencies until they match the AC frequency at which point the ions are ejected. Generally, the resolution of the former method is poorer, which is discussed in depth in a previous paper on secular frequency scan mass calibration [12].

Figure 5 demonstrates increase in mass resolution in secular frequency scanning by using a successive resonance method for a mixture of three quaternary ammonium ions. In this case, however, the secular or sideband frequencies must both be ramped as a function of time while the rf amplitude is fixed. The increase in resolution in the successive resonance secular scan is remarkable, ranging from 3 to 5×. We again note that the resolution improvement is highest for those ions ejected first (low mass ions), indicating the role of space charge.

Successive resonance secular frequency scanning. The blue trace is the mass spectrum obtained from a single resonance secular frequency scan from 200 to 100 kHz, 1 Vpp. The red trace is the result of a successive resonance secular frequency scan using an additional simultaneous sweep from 200.04 kHz to 100.04 kHz with an amplitude of 1.4 Vpp. Analytes were quaternary ammonium ions m/z 284, 360, and 382

Although it is not shown here, successive resonances may be most applicable to improving the performance of miniature mass spectrometers, which tend to suffer from lower resolution and higher space charge effects than benchtop instruments [32, 33].

Conclusion

The resolution of a benchtop ion trap is more than tripled using successive resonance ejection at arbitrarily chosen static and dynamic frequencies. The resolution improvement is attributed largely to decreased space charge effects during ejection when the ions are first excited to amplitudes beyond the rest of the ion cloud. Because the mechanism does not depend on higher order fields for resolution improvement, additional hexapole and octopole resonances are not needed in this method. Isotope ratios in the successive resonance scans can differ from those obtained by single frequency resonance ejection, likely due to the different phase relationships between the rf and AC waveforms as each ion is ejected. In addition, beat frequencies that develop from the sum of two sinusoids may play a role in the resolution improvement.

This paper is complemented by parallel work in ion isolation using dual frequencies with high amplitudes [34] and broadband ion activation using a fixed AC amplitude and scanning the rf amplitude in the reverse direction [35]. This emerging set of techniques makes up a unique package that addresses every step of the MS/MS experiment.

Notes

Acknowledgments

The researched presented herein was supported by NASA (Award NNX16AJ25G).